[Paper Review] OPERA Superluminal Neutrinos per Quantum Trajectories

Edward R. Floyd|arXiv (Cornell University)|Dec 20, 2011

Neutrino Physics Research11 references3 citations

TL;DR

This paper proposes that superluminal neutrino propagation observed in the OPERA experiment can be explained by quantum trajectories incorporating self-entanglement via internal backscatter, where nonlocality from coherent interference of spectral components leads to overall superluminal transit times. The model shows that favorable biasing of phase constants can produce theoretical neutrino velocities matching OPERA's reported 2.37×10⁻⁵ superluminal excess, consistent with quantum Hamilton-Jacobi formalism and neutrino oscillation mechanisms.

ABSTRACT

Quantum trajectories are used to study OPERA findings regarding superluminal neutrinos. As the applicable stationary quantum Klein-Gordon equation is real, real quantum reduced actions and subsequent real quantum trajectories follow. The requirements for superluminal neutrinos are examined. A neutrino that is self-entangled by its own backscatter is shown to have a nonlocal quantum trajectory that may generate a superluminal transit time. Various cases are shown to produce theoretical superluminal neutrinos consistent with OPERA neutrinos. Quantum trajectories are also shown to provide insight into neutrino oscillations.

Motivation & Objective

• To explain the OPERA experiment's reported superluminal neutrino results through a quantum trajectory framework that preserves internal entanglement.
• To investigate how self-entanglement from internal backscatter can generate nonlocal quantum motion leading to superluminal transit times.
• To determine whether systematic biases in phase constants could account for the observed superluminal signal without violating relativity.
• To explore the connection between backscatter-induced interference and neutrino oscillation mechanisms.
• To assess the consistency of the model with known constraints, such as those from Cohen and Glashow, particularly at temporal turning points.

Proposed method

• The study uses the relativistic quantum Hamilton-Jacobi formulation of the stationary Klein-Gordon equation to derive real quantum reduced actions and trajectories.
• A general solution for the quantum reduced action W(q) is constructed using real independent solutions of the SKGE and a Möbius transformation with real coefficients (A, B, C, D).
• Backscatter is modeled as a counter-propagating spectral component within a dichromatic wavefunction, contributing to self-entanglement and nonlocal motion.
• The quantum trajectory's velocity is evaluated via the quantum factor H_Q, which depends on the phase shift φ and the backscatter parameter β.
• Interference effects between spectral components are weighted by the Born probability |ψ|², and the average over φ is computed to assess net superluminal behavior.
• The model examines how systematic biases in φ or β can favor constructive interference, leading to observable superluminal transit times.

Experimental results

Research questions

• RQ1 Can quantum trajectories with internal backscatter produce superluminal transit times consistent with the OPERA experiment's reported 2.37×10⁻⁵ velocity excess?
• RQ2 How does self-entanglement from backscatter contribute to nonlocal motion and overall superluminal behavior in quantum trajectories?
• RQ3 What role does the phase shift φ play in determining whether a trajectory is superluminal, and can systematic biasing of φ explain the experimental result?
• RQ4 How does the model account for neutrino oscillations, and what is the physical interpretation of ν,ν̄ pair creation/annihilation at temporal turning points?
• RQ5 Are the predictions of this model consistent with the Cohen and Glashow constraints on superluminal neutrinos?

Key findings

• The model predicts a relative velocity excess of 2.37×10⁻⁵ for neutrinos with internal backscatter, matching the OPERA observation when the backscatter parameter β is set to 3.442×10⁻³.
• Superluminal propagation arises from coherent interference between forward and backscattered spectral components, with nonlocality enabling overall superluminal transit despite subluminal segment velocities.
• A favorable bias in the phase shift φ is required for superluminal behavior; uniform averaging over φ suppresses superluminality, indicating the need for systematic selection of quantum motion constants.
• Neutrino oscillations are explained by ν,ν̄ pair creation at local time minima and annihilation at local time maxima of the quantum trajectory.
• The model avoids Cohen and Glashow constraints because these apply only to subluminal or superluminal segments, not to the full trajectory where energy is conserved and the full nonlocal motion is considered.
• The backscatter parameter β controls the degree of superluminality, with higher β values increasing the velocity excess beyond a threshold.